Did You Know? Someone Else Wrote Maxwell’s Equations

The truth behind those well-known formulas

Another in a series of “Did You Know?” articles that uncover interesting historical, technical, and IEEE-related factoids.

One often hears the cliché “a musician’s musician,” or “a poet’s poet.” Well, if there was an engineer’s engineer, it was probably Oliver Heaviside [above].

When Michael Pupin invented the loading coil to improve telephone transmission in 1899, it was based explicitly on the work of Heaviside more than a decade earlier. Guglielmo Marconi transmitted and received a radio signal beyond the horizon in 1901, and Heaviside explained a year later how it was possible. And, most importantly, James Clerk Maxwell established the laws of electromagnetism, but Heaviside rewrote them so they could be better understood and applied.

Heaviside, the nephew of the electrical pioneer Charles Wheatstone, was born in London in 1850. Tutored at home and mostly self-taught in his home laboratory, he took a job in 1868 as a telegraph operator—which gave him experience with the emerging electrical science and engineering fields in which his uncle was a leading light. Within six years, Heaviside had enough experience to return to his laboratory, and he began a remarkable career in electrical engineering, despite never holding a professional position.

Oliver Heaviside worked with his uncle, Charles Wheatstone, who popularized the Wheatstone bridge (shown above). Photo: IEEE History Center

His first work that drew the public’s attention was the formulation of the telegrapher’s equations, which define the behavior of an electrical transmission line. That work led him in 1880 to invent and patent coaxial cable, which is still used today. He next made a splash developing operational calculus, the technique whereby one solves differential equations—a frequent need in engineering—by transforming them into polynomial equations that can be solved algebraically. The mathematicians of the time were suspicious of the rigor of his methods, but he was able to use his mathematical techniques to make his greatest contribution yet.

Every electrical engineer is aware of Maxwell’s equations: four mathematical expressions that in elegant form explain the full behavior of electromagnetism—and grace many an engineering school sweatshirt. However, many are not aware that between 1860 and 1861, Maxwell actually developed a set of 20 equations to explain electromagnetic radiation, and they included terms for both fields and potentials.

Heaviside, along with a few contemporaries, was a firm believer in Maxwell’s approach to understanding electromagnetism, but their complexity made the equations difficult to apply. So, using a new notation, Heaviside simplified Maxwell’s original equations to the four, using only terms for fields that we employ to this day. At first those equations were referred to by various combinations of the names of Maxwell, Heaviside, and Heinrich Hertz, who was the first to demonstrate Maxwell’s waves. However, for all his otherwise brilliance, Albert Einstein referred to them as Maxwell’s equations in his 1940 monograph “Considerations Concerning the Fundamentals of Theoretical Physics.” The name stuck, and Heaviside faded from public view. (Hertz at least had a unit named after him.)

Nevertheless, Heaviside was recognized in his own lifetime. As a result of his work on Maxwell’s equations and his other contributions, in 1891 he was made a Fellow of the U.K.'s Royal Society, unusual for an “amateur” engineer at the end of the 19th century. And in 1922, the Institute of Electrical Engineers in the U.K. (today known as the Institution of Engineering and Technology) awarded him its first Faraday Medal, which recognizes achievements in engineering, science, and technology. His name is also given to a layer of ionized gases in the atmosphere.

Heaviside died in 1925 in Devon, England, in genteel poverty, having received little profit or broader name recognition from his vast contributions to technology and to society.

This article has been corrected from a previous version

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